an exponential distribution to the data

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Assume that a reliability engineer fits a half-logistic distribution to the failure data given in . An additional reliability test is conducted and the following data are obtained: 1500, 2000, 2200, 2800, 3500, 3900, 4500, 4900, 5200, 5750, 6125, 6680, 7125, 7795, 8235, 8699, 9000+ , 9000+ , 9000+ . The sign “+” indicates censoring. The engineer fits an exponential distribution to the data. Realizing that some of the data fitted by the half-logistic distribution exhibits an increasing hazard rate and that the data fitted by the exponential distribution exhibits a constant hazard rate, the engineer decides to combine the two data sets and fit them using one distribution. In doing so, the hazard rate of the mixture may exhibit a decreasing failure rate.
(a) Determine the conditions that result in a decreasing hazard rate (if it exists in this case).
(b) What is the estimated MTTF based on the mixed distribution?

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